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3 years ago

Solve the system equations. X+2y=0 10y=-5

Mathematics

1 answer:

nexus9112 [7]3 years ago

5 0

Answer:

x=1

y=-1/2

Step-by-step explanation:

x+2y=0....(1)

10y=-5.....(2)

From (2) we can find y.

y=-5/10

y=-1/2

Use that in (1)

x+2*(-1/2)=0

x-1=0

x=1

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Select the correct answer for each statement. (k+2, k+3 , k+4) or (k+10, k+12, k+14) will yield consecutive odd integers. (k+6,

almond37 [142]

Answer:

Step-by-step explanation:

one

The only really certain way of getting an odd integer is to do 2k + 1. Therefore the answer should be something like 2k+1, 2k+3, 2k + 5

The best I can do for the first one is to assume that k is odd and that the answer is k + 10, k+12, k+14, but I would ask your instructor if this is merely the best answer out of a poor lot or if the question really has no answer.

Two things should be noted.

1. k has to be odd.

2. The first choice has to give consecutive integers because what is added on is 2 3 and 4. Those numbers are consecutive.

Two

k+1, k+2, k+3. See point 2 above. k is a constant and any number. 1,2,3 are consecutive so the results are consecutive. Even if k < 0 the numbers will be consecutive.

k= - 10

k+1 = - 9

k+2 = -8

k+3 = - 7

These are consecutive.

Your first choice will give either consecutive odd or even numbers depending on what k is.

If k = even, then k+6, k+ 8, k+10 will all be even.

If k = odd then the givens will be odd.

4 0

3 years ago

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How to find the square root of complex numbers?? Find the square root of (6+8i) ??

ivann1987 [24]

Answer:

$2 \sqrt{2} + i \sqrt{2}$

Step-by-step explanation:

The square of a complex number is a complex number. Here, we have:

${(a + bi)}^{2} = 6 + 8i$

${a}^{2} + 2abi - {b}^{2} = 6 + 8i$

We then have this system of equations:

${a}^{2} - {b}^{2} = 6$

$2ab = 8$

Solving this system:

$ab = 4$

$b = \frac{4}{a}$

${a}^{2} - {( \frac{4}{a}) }^{2} = 6$

${a}^{2} - \frac{16}{ {a}^{2} } = 6$

${a}^{4} - 16 = 6{a}^{2}$

${a}^{4} - 6 {a}^{2} - 16 = 0$

$( {a}^{2} - 8)( {a}^{2} + 2) = 0$

${a}^{2} = 8$

$a = 2 \sqrt{2}$

$b = \frac{4}{2 \sqrt{2} } = \sqrt{2}$

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2 years ago

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Use Euclid’s Ladder (or a factor tree) to write the prime factorization.

Veseljchak [2.6K]

Answer:

Step-by-step explanation:

the answer is 64 hope this helps

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3 years ago

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If cos() = − 2 3 and is in Quadrant III, find tan() cot() + csc(). Incorrect: Your answer is incorrect.

nydimaria [60]

Answer:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

Step-by-step explanation:

Given

$\cos(\theta) = -\frac{2}{3}$

$\theta \to$ Quadrant III

Required

Determine $\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

We have:

$\cos(\theta) = -\frac{2}{3}$

We know that:

$\sin^2(\theta) + \cos^2(\theta) = 1$

This gives:

$\sin^2(\theta) + (-\frac{2}{3})^2 = 1$

$\sin^2(\theta) + (\frac{4}{9}) = 1$

Collect like terms

$\sin^2(\theta) = 1 - \frac{4}{9}$

Take LCM and solve

$\sin^2(\theta) = \frac{9 -4}{9}$

$\sin^2(\theta) = \frac{5}{9}$

Take the square roots of both sides

$\sin(\theta) = \±\frac{\sqrt 5}{3}$

Sin is negative in quadrant III. So:

$\sin(\theta) = -\frac{\sqrt 5}{3}$

Calculate $\csc(\theta)$

$\csc(\theta) = \frac{1}{\sin(\theta)}$

We have: $\sin(\theta) = -\frac{\sqrt 5}{3}$

So:

$\csc(\theta) = \frac{1}{-\frac{\sqrt 5}{3}}$

$\csc(\theta) = \frac{-3}{\sqrt 5}$

Rationalize

$\csc(\theta) = \frac{-3}{\sqrt 5}*\frac{\sqrt 5}{\sqrt 5}$

$\csc(\theta) = \frac{-3\sqrt 5}{5}$

So, we have:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \tan(\theta) \cdot \frac{1}{\tan(\theta)} + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 + \csc(\theta)$

Substitute: $\csc(\theta) = \frac{-3\sqrt 5}{5}$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 -\frac{3\sqrt 5}{5}$

Take LCM

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

6 0

3 years ago

A line that includes the points (n,-6) and (-9,-4) has a slope of -15. What is the value of n?

pav-90 [236]

Answer:

n=-8.86

Step-by-step explanation:

Slope will determine the direction and the steepness of a function. It could be either increasing/decreasing depend on minus or plus. The formula for slope is

m= (y2-y1)/ (x2-x1)

If you add (n,-6) and (-9,-4) to the equation, it will be:

m= (y2-y1)/ (x2-x1)

-15= (-6--4)/ (n--9)

-15= (-2)/ (n+9)

-15(n+9) = -2

-15n - 135=-2

-15n= -2 + 135

n= -133/15

n= -8 13/15= -8.86

7 0

3 years ago